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A space-time integral estimate for a large data semi-linear wave equation on the Schwarzschild manifold | | P. Blue
; A. Soffer
; | | Date: |
13 Mar 2007 | | Subject: | Analysis of PDEs | | Abstract: | We consider the wave equation (-dt^2+dr^2 -V -V_L(-Delta_{S^2})) u = fF’( u ^2) u with (t,
ho, heta,phi) in R x R x S^2. The wave equation on a spherically symmetric manifold with a single closed geodesic surface or on the exterior of the Schwarzschild manifold can be reduced to this form. Using a smoothed Morawetz estimate which does not require a spherical harmonic decomposition, we show that there is decay in L^2_{loc} for initial data in the energy class, even if the initial data is large. This requires certain conditions on the potentials V, V_L, and f. We show that a key condition on the weight in the smoothed Morawetz estimate can be reduced to an ODE condition, which is verified numerically. | | Source: | arXiv, math/0703399 | | Services: | Forum | Review | PDF | Favorites | |
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